For a given set $S\subseteq \mathbb {Z}_m$ and $\overline {n}\in \mathbb {Z}_m$ , let $R_S(\overline {n})$ denote the number of solutions of the equation $\overline {n}=\overline {s}+\overline {s'}$ with ordered pairs $(\overline {s},\overline {s'})\in S^2$ . We determine the structure of $A,B\subseteq \mathbb {Z}_m$ with $|(A\cup B)\setminus (A\cap B)|=m-2$ such that $R_{A}(\overline {n})=R_{B}(\overline {n})$ for all $\overline {n}\in \mathbb {Z}_m$ , where m is an even integer.

To address the challenges of limited language proficiency and provide necessary feedback in the implementation of task-based language teaching (TBLT), a mobile-supported TBLT application was developed to provide linguistic and task scaffolding. Sixty-six English as a foreign language (EFL) university learners participated in a three-week experiment as part of a general English course. They were assigned to either an experimental group (mobile-supported TBLT), which received TBLT with scaffolds built into the application, or a control group (traditional TBLT), which received traditional paper-based TBLT without the scaffolds. At the end of the experiment, an English achievement test of vocabulary, grammar, and conversation comprehension was administered to determine if the technological scaffolds enhanced the learning outcomes for the course. Students’ self-perceived use of oral communication strategies was also measured to explore how these scaffolds affected the conversational interaction essential for task performance. Results showed that the mobile-supported TBLT group outperformed the traditional TBLT group on the vocabulary and conversation comprehension tests but not so much on the grammar test. Also, the mobile-supported TBLT group reported greater awareness of fluency- and accuracy-oriented strategies for speaking than the traditional TBLT group. Implications for designing mobile learning to enhance TBLT in an EFL setting are drawn.

Renal fibrosis is common especially in the elderly population. Recently, we found that vitamin D deficiency caused prostatic hyperplasia. This study aimed to investigate whether vitamin D deficiency promotes renal fibrosis and functional impairment. All mice except controls were fed with vitamin D deficient (VDD) diets, beginning from their early life. The absolute and relative kidney weights on postnatal week (PNW)20 were decreased in VDD diet-fed male pups but not in female pups. A mild pathological damage was observed in VDD diet-fed male pups but not in females. Further analysis showed that VDD-induced pathological damage was aggravated, accompanied by renal disfunction in 40-week-old male pups. An obvious collagen deposition was observed in VDD diet-fed 40-week-old male pups. Moreover, renal α-SMA, a marker of epithelial-mesenchymal transition (EMT), and Tgf-β mRNA were upregulated. The in vitro experiment showed that 1,25(OH)2D3 alleviated TGF-β1-mediated downregulation of E-cadherin and inhibited TGF-β1-evoked upregulation of N-cadherin, vimentin and α-SMA in renal epithelial HK-2 cells. Moreover, 1,25(OH)2D3 suppressed TGF-β1-evoked Smad2/3 phosphorylation in HK-2 cells. These results provide experimental evidence that long-term vitamin D deficiency promotes renal fibrosis and functional impairment, at least partially, through aggravating TGF-β/Smad2/3-mediated EMT in middle-aged male mice.

A suite of Jurassic–Cretaceous migmatites was newly identified in the Liaodong Peninsula of the eastern North China Craton (NCC). Anatexis is commonly associated with crustal thickening. However, the newly identified migmatites were formed during strong lithospheric thinning accompanied by voluminous magmatism and intense deformation. Field investigations show that the migmatites are spatially associated with low-angle detachment faults. Numerous leucosomes occur either as isolated lenses or thin layers (dykes), parallel to or cross-cutting the foliation. Peritectic minerals such as titanite and sillimanite are distributed mainly along the boundaries of reactant minerals or are accumulated along the foliation. Most zircons show distinct core–rim structures, and the rims have low Th/U ratios (0.01–0.24). Zircon U–Pb dating results indicate that the protoliths of the migmatites were either the Late Triassic (224–221 Ma) diorites or metasedimentary rocks deposited sometime after c. 1857 Ma. The zircon overgrowth rims record crystallization ages of 173–161 Ma and 125 Ma, which represent the formation time of leucosomes. These ages are consistent with those reported magmatic events in the Liaodong Peninsula and surrounding areas. The leucosomes indicate a strong anatectic event during the Jurassic–Cretaceous period. Partial melting occurred through the breakdown of muscovite and biotite with the presence of water-rich fluid under a thermal anomaly regime. The possible mechanism that caused the 173–161 Ma and 125 Ma anatectic events was intimately related to the regional crustal extension during the lithospheric thinning of the NCC. Meanwhile, the newly generated melts further weakened the rigidity of the crust and enhanced the extension.

A higher dietary intake or serum concentration of betaine has been associated with greater lean body mass in middle-aged and older adults. However, it remains unknown whether betaine intake is associated with age-related loss of skeletal muscle mass (SMM). We assessed the association between dietary betaine intake and relative changes in SMM after 3 years in middle-aged adults. A total of 1242 participants aged 41–60 years from the Guangzhou Nutrition and Health Study 2011–2013 and 2014–2017 with body composition measurements by dual-energy X-ray absorptiometry were included. A face-to-face questionnaire was used to collect general baseline information. After adjustment for potential confounders, multiple linear regression found that energy-adjusted dietary betaine intake was significantly and positively associated with relative changes (i.e. percentage loss or increase) in SMM of legs, limbs and appendicular skeletal mass index (ASMI) over 3 years of follow-up (β 0·322 (se 0·157), 0·309 (se 0·142) and 0·303 (se 0·145), respectively; P < 0·05). The ANCOVA models revealed that participants in the highest betaine tertile had significantly less loss in SMM of limbs and ASMI and more increase in SMM of legs over 3 years of follow-up, compared with those in the bottom betaine tertile (all Ptrend < 0·05). In conclusion, our findings suggest that elevated higher dietary betaine intake may be associated with less loss of SMM of legs, limbs and ASMI in middle-aged adults.

The Wulian complex is located on the northern margin of the Sulu orogenic belt, and was formed by collision between the North China Craton (NCC) to the north and South China Craton (SCC) to the south. It consists of the metasedimentary Wulian Group, gneissic granite and meta-diorite. The U–Pb analyses for the detrital zircons from the Wulian Group exhibit one predominant age population of 2600–2400 Ma with a peak at c. 2.5 Ga and several secondary age populations of > 3000, 3000–2800, 2800–2600, 2200–2000, 1900–1800, 1500–1300 and 1250–950 Ma; some metamorphic zircons have metamorphic ages of c. 2.7, 2.55–2.45, 2.1–2.0 and 1.95–1.80 Ga, which are consistent with magmatic-metamorphic events in the SCC. Additionally, the Wulian Group was intruded by the gneissic granite and meta-diorite at c. 0.76 Ga, attributed to Neoproterozoic syn-rifting bimodal magmatic activity in the SCC and derived from partial melting of Archaean continental crust and depleted mantle, respectively. The Wulian Group therefore has tectonic affinity to the SCC and was mainly sourced from the SCC. The detrital zircons have positive and negative ϵHf(t) values, indicating that their source rocks were derived from reworking of both ancient and juvenile crustal rocks. The major early Precambrian crustal growth took place during c. 3.4–2.5 Ga with a dominant peak at 2.96 Ga and several secondary peaks at 3.27, 2.74 and 2.52 Ga. The two oldest zircons with ages of 3307 and 3347 Ma record the recycling of ancient continental crust (> 3.35 Ga) and crustal growth prior to c. 3.95 Ga in the SCC.

Starch content is an important trait in barley. To evaluate the genetic diversity and identify molecular markers of starch content in barley, 40 cultivated barley genotypes collected from different regions, including genotypes whose starch content is at either the high or low end of the spectrum (15), were used in this study. All the genotypes were re-sequenced by the double-digest-restriction associated DNA sequencing method, and a total of 299,103 single-nucleotide polymorphism (SNP) markers were obtained. The genotypes were divided into four sub-populations based on FASTSTRUCTURE, principal component analysis and neighbour-joining tree analysis. All four sub-populations had a high linkage disequilibrium, especially group 3, whose members were recently bred for malting in the Jiangsu coastal area. The starch content of the barley lines was evaluated during three growing seasons (2014–2017), and the average values of starch content across the three growing seasons at the low and high ends were 51.5 and 55.0%, respectively. The starch content was affected by population structure, the barley in group 2 had a low starch content, while the barley in group 4 had a high starch content. Twenty-six SNP markers were identified as being significantly associated with starch content (P ⩽ 0.001) based on the average values across the three growing seasons using the mixed linear model method. These SNP markers were located on chromosomes 1H and 4H, and were considered loci of qSC1-1 and qSC4-1, respectively. The major identified QTLs for starch content are helpful for further research on carbohydrates and for barley breeding.

This study focuses on the process of the circulation deposition in the Richtmyer–Meshkov instability (RMI). The growth rate of circulation and its sources are theoretically and numerically studied to reveal the physical mechanism of the viscosity in the circulation deposition process. We derive a predicting model of the circulation rate for RMI. More importantly, all the contributing sources are separately predicted. Particularly, the viscous source, which previously lacked theoretical or numerical investigations, is efficiently predicted. The RMI problems in a large range of initial conditions are simulated with the direct simulation Monte Carlo (DSMC) method to verify our predicting model and further reveal the circulation deposition mechanism. The DSMC simulations provide reliable quantification of the circulation deposition (especially viscous contribution) for RMI due to its molecular nature. Our model predicts the circulation rate, baroclinic and viscous sources accurately for all the cases in comparison with the simulations. A new physical insight into the mechanism of viscosity in RMI is provided. Unlike the previous understandings that nearly all circulation deposition in RMI comes from the baroclinic source, this study reveals the hidden positive contribution of the viscous source, especially for high Mach number conditions (up to 11 % of total circulation rate). For RMI, the large viscosity gradient inside the shock waves plays a crucial role in the circulation deposition even under high Reynolds number conditions. Our study also provides exciting opportunities to further understand the viscous contribution to the vorticity dynamics in the reshocked RMI and shock wave–turbulence interactions.

HIV-1 drug resistance can compromise the effectiveness of antiretroviral therapy (ART). A survey of pretreatment HIV-1 drug resistance (PDR) was conducted in Lincang Prefecture of Yunnan Province. From 372 people living with HIV/AIDS initiating ART for the first time during 2017–2018, 322 pol sequences were obtained, of which 11 HIV-1 strain types were detected. CRF08_BC (70.2%, 226/322) was the predominant strain, followed by URF strains (10.6%, 34/322). Drug resistance mutations (DRMs) were detected among 34.2% (110/322) of the participants. E138A/G/K/R (14.3%, 46/322) and V179E/D/T (13.7%, 47/322) were the predominant DRMs. Specifically, E138 mutations commonly occurred in CRF08_BC (19.9%, 45/226). Among the DRMs detected, some independently conferred resistance, such as K65R (1.6%, 5/322), Y188C/F/L (0.9%, 3/322), K103N (0.6%, 2/322) and G190A (0.3%, 1/322), which conferred high-level resistance. The prevalence of PDR was 7.5% (95% CI: 4.6–10.3%) and the prevalence of non-nucleotide reverse transcriptase inhibitor (NNRTI) resistance was 5.0% (95% CI: 2.6–7.4%), which is below the threshold (⩾10%) of initiating a public health response. In conclusion, HIV-1 genetic diversity and an overall moderate level of PDR prevalence were found in western Yunnan. PDR surveillance should be continually performed to decide whether a public health response to NNRTI resistance should be initiated.

Infants attune to their native language during the first two years of life, as attested by decreases in the processing of nonnative phonological sounds and reductions in the range of possible sounds accepted as labels for native words. The present study shows that French-learning infants aged 1;8 can learn new words in an unfamiliar language, Cantonese, after just 6 repetitions of each word. This shows that word learning in a nonnative language remains possible during the second year of life even in a nonnative language that is typologically distinct from the native language.

The present study examined the relationship between the Lie scale scores and striatal D2/D3 receptor availability with respect to the cerebellum in 42 healthy community volunteers in Taiwan using single photon emission computed tomography (SPECT) with [123I]iodo-benzoaminde (IBZM). Even after controlling of age and educational level, subjects' Lie scale scores of the Maudsley personality inventory correlate negatively with D2/D3 receptor availability. Individual with higher Lie scale scores may have higher impulsivity due to lower dopaminergic availability.